Methods for calculating errors of a function whose arguments have individual errors.

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13 views

Propagating uncertainties using random forest out-of-bag accuracy estimates

Let's say I train a random forest on some data and get an out-of-bag accuracy estimate of 90%. I then predict a quantity using this trained forest. What should be the uncertainty I give to that ...
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1answer
35 views

How to combine two measurements of the same quantity with different confidences in order to obtain a single value and confidence

Back in the lab at university, we were taught to measure the quantity of interest some number of times (call this N), and then calculate the standard error. The underlying assumption here is that you ...
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2answers
16 views

Adding Up Margins of Error

I'd like to add data from Census.gov, but I don't know how to add up the Margin of Error. Example, I have the estimate number of renters in Congressional District 1, (203,941 +/- 4,892) and the same ...
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0answers
16 views

Propagation of uncertainty when both axes depend on same variables

I have a data set y as a function of t measured at a distance L. Both t and L have a known standard deviation (i.e. the relative error on t changes with t). What I am now trying to do is to define a ...
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47 views

Monte Carlo error propagation

Consider a set $X$ of $N$ iid random variables, each one with its own standard deviation: $$X: \{x_1\pm\sigma_1, x_2\pm\sigma_2, ..., x_N\pm\sigma_N\}$$ Say I have a "black box" numerical function ...
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1answer
16 views

Error propagation in a linear model

I am currently interested in learning more on error propagation. At the moment I am trying to find out how to calculate the uncertainty of a value that is obtained from a linear model. For the linear ...
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0answers
21 views

Propagation of error in matrix multiplication involving an inversion

Hi I have a system $a$ = $B^{-1}x$ where $a$ and $x$ are 9x1 vectors and $B$ is a 9x9 matrix to be inverted Each element in $B$ is a product of two values with their own uncertainties and the vectors ...
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10 views

Serial dilution error propagation

How does serial dilution minimise the occurrence of experimental error? Does it not increase/propagate imprecision?
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6 views

Theoretically is model of error as erroneous as the erro itself?

I'm teaching a response model [i_1,i_2,...,i_n] --> <-1,1> i_n is <-1,1> I have chosen recurrent neural network but this might have nothing to do with my question. I will compare model with ...
2
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27 views

Do Monte Carlo perturbations capture all the uncertainty in prediction?

I have a model $M$ that I use to predict a value $y = M(\vec x)$. I have known one-$\sigma$ error bars on each input $x_i \in \vec x$. I want to know the one-$\sigma$ error bar on my prediction $y$. ...
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28 views

Error propagation with dependent variables

I've posted this in physics but without much help that I can apply to my problem. Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from ...
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29 views

How to propagate uncertainty into the prediction of a neural network?

I have inputs $x_1\ldots x_n$ that have known $1\sigma$ uncertainties $\epsilon_1 \ldots \epsilon_n$. I am using them to predict outputs $y_1 \ldots y_m$ on a trained neural network. How can I obtain ...
3
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1answer
27 views

Propagate uncertainty of a parameter through a function

Suppose I have a probability distribution (in fact I've got a nice case where that distribution is Gaussian) on a parameter value. e.g. the parameter $x$ has $\mu = 3$ and $\sigma^2 = 1$. Now suppose ...
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0answers
18 views

Measuring Prediction vs Actual Difference

To find error we usually measure our predicted y vs actual y. Are there any error terms that measure the error in y AND the error in x, given y? In the image below the line is doing a pretty good ...
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0answers
22 views

Error propagation of correlated data

I have a dataset of 1-hour averages of a variable measured throughout a year. The goal is to get the sum of that variable for the entire year. Each 1-hour average has an error value associated with ...
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23 views

Estimating errors from optimization? (Genetic algorithm or otherwise)

I have a vector of observations $\vec x_{\text{obs}}$ that have been measured with known uncertainties $\vec \sigma_{x}$. I have a model $f$ that takes parameters $\vec \theta$ and produces values ...
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13 views

How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
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3answers
193 views

Variance of an average of random variables

This seems like it should be a pretty common problem. I have four estimates of fishing effort, each with its own variance. For subsequent calculations, I want the mean of the four estimates, and a ...
2
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1answer
56 views

Are the parameters of Non-linear regression independent of each other?

I'm propagating error in the parameters determined by the following growth function... $$ \hat{y} = ae^\frac{t}{b} + (1- a)e^\frac{t}{c} $$ Say I have another model that uses the parameters {a,b,c} ...
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1answer
101 views

Backpropagation with Cross-entropy Cost Function

I'm using the cross-entropy cost function for backpropagation in a neutral network as it is discussed here: ...
2
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1answer
752 views

Cross-entropy Cost Function in Neural Network

I'm looking at the cost function found here: http://neuralnetworksanddeeplearning.com/chap3.html#introducing_the_cross-entropy_cost_function What are we summing over in: C= −1/n ∑x ...
0
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1answer
44 views

Error propagation and relative error

Say I have measured the value A = 50 +- 2 and from this I am calculating the value: B(A) = A^2 From what I understand I calculate the new error using error propagation to be delta_B ...
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29 views

How to consider propagated measurement errors and “statistical errors”

I come from an Engineering background, and I am familiar with some basics of error treatment. However, discussing with a friend over some data he had to analyze, we couldn't quite figure out what to ...
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17 views

Representing error when there are multiple different, linked error sources

Suppose I make some measurements of variable $X_i$ in separate experiments, and each has some error. In a separate (single) experiment I measure $b$ which is independent of $X_i$ but shared between. ...
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91 views

What is the correct way to interpolate error?

If I have a 2-D data, say $y = f(x)$, with error in the dependent variable, $\delta y$ in this case, and I want to interpolate this data set to a coarser independent variable grid, $x$, what is the ...
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57 views

Adding numbers with asymmetric uncertainties

I need to add a series of numbers with asymmetric standard deviations, such as $$5_{-2}^{+1} \,+ \,3_{-3}^{+1}.$$ Although I know it's common to add the upper errors ($\sigma_{\scriptsize{+}}$) and ...
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20 views

Propagation of uncertainties in functions not continuously differentiable

According to the Guide to the Expression of Uncertainty in Measurement as published by the Bureau International des Poids et Mesures (BIPM), the combined standard uncertainty $u_c^2$ for a function $y ...
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1answer
78 views

Disadvantages of uncertainty in modeling

I am preparing a presentation, my work mainly concentrates on uncertainty and sensitivity analysis. I was wondering if I can convince my audience by the importance of studying uncertainty in modeling. ...
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15 views

Back propagation of Uncertainty

I am recently working on the subject of uncertainty. I read that uncertainty analysis and sensitivity analysis are important topics in this domain(the first is ti do a forward propagation of ...
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0answers
35 views

How would I average noisy data representing the noise using error bars?

I have data that was binned in a process that provides the average and standard deviation for the values in each bin. For some of the data, the variation between bins is significantly larger than the ...
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0answers
47 views

Uncertainty of sum of values estimated through linear regression

I have a continuous record of a variable X, which I want to use as a surrogate for another system value Y. I have a number of measurements of Y, which I can plot against concurrent measurements of X ...
0
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1answer
27 views

Propagating RMSECV?

I have two regression models, each of which has an associated root mean squared error of cross validation (RMSECV). I would like to combine the results of the models using a weighted average to get a ...
0
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1answer
46 views

Backward propagation algorithm demonstration in neural networks: any VERY-SMALL-STEP by VERY-SMALL-STEP demonstration?

I'm looking for a VERY DETAILED demonstration for the backward propagation algorithm in neural networks machine learning. Specifically the step below. I've got the excellent Michael Nielsen ...
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30 views

backpropagation: why find the global minimum instead of the value of zero

in back propagation, you use gradient descent to find the stationary point on the equation of the Error = (in terms of weight). But don't we want the error to be equal to zero? if the error is zero, ...
0
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1answer
26 views

Gini index on data with error margins

I have data series and I want to calculate Gini coefficients for each row as an estimate of matrix sparsity. Hoever values contained in the rows are not exact and have error bounds. My question is ...
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0answers
32 views

Error propagation and Standard Deviation

I never quite got the hang of this during my entry stat course and it has been bugging me for a long time now. Lets assume I'm trying to find the focal length of a concave lens. Using a mockup ...
3
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0answers
101 views

Propagation of uncertainty (intersection of two graphs)

The situation is as follows: I performed necessary measurements and used them to create two graphs. I used polynomial regression to find the point of intersection. What I know: precision of ...
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69 views

Trying to impelement IRPROP+

I'm stuck I tried 3 times to setup IPROP+. I figured IPROP+ was the most highly rated of the three found here http://heatonresearch.com/wiki/RPROP Problem is... my training doesn't seem to work. ...
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361 views

Entropy, Softmax and the derivative term in Backpropagation

I'm currently interested in using Cross Entropy Error when performing the BackPropagation algorithm for classification, where I use the Softmax Activation Function in my output layer. From what I ...
0
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0answers
101 views

Propogation of error in a matrix inversion

I'm trying to find the deterministic error bounds for some parameters calculated through distance geometry. The equation can be simplified to the following form: $ \left[\begin{matrix} x_1 \\ x_2 \\ ...
0
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1answer
36 views

The probability of m out of K things being wrong with an error of ɛ

I have a homework question about a machine-learning algorithm that uses ensemble learning with simple majority voting. Assuming we have K hypotheses, each with an error ɛ, the question asks us to ...
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1answer
150 views

What does correlation mean in error propagation?

From the python uncertainties package: Correlations between expressions are correctly taken into account. Thus, x-x is exactly zero, for instance (most implementations found on the web yield a ...
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1answer
89 views

Error propagation - nonnormal (again)

I have a dataset of ~2000 points. Each of those points has a standard error value associated with it, and it is assumed that the data points and errors are uncorrelated. Both the dataset and the ...
4
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0answers
77 views

propagation of standard error in a sum of proportions

I am new to error propagation, and I am trying to solve a simple problem: I am trying to calculate the estimate and standard error of a parameter (carbon density) across a landscape composed of ...
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0answers
55 views

propagation of the error in the summation

I have a question regarding the propagation of the error during the summation. Please see the equation below. In this equation only quantity R has an error. How it will propagate to the final value ...
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0answers
44 views

Error propagation and p value

Say I have parameters $a(x$) and $b(x)$, with $N_a(x)$ and $N_b(x)$ experimental measurement counts, respectively. $x$ is an independent variable ($x_1, x_2, ...$). For each $a$ and $b$, I can ...
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0answers
37 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
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2answers
486 views

Background subtraction for signal and error analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
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2answers
352 views

Error for combining multiple binomial distributions

This problem is somewhat involved and I have a partial solution so bear with me. I will illustrate the problem with an example. Lets say we have two processes and we want to know which has a higher ...
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0answers
143 views

Propagation of Poisson Confidence Intervals

I have a set of measurement with 95% Poisson confidence intervals, and I would like to subtract and multiply them and propagate the error. For example, I measured the copy number of a piece of DNA in ...